Radians and the Quest to find Theta

I attached a scan of the question giving me trouble as it has a helpful drawing - basically I have to find the radius and height of the cone, and angle of inclination, when the original angle of the radian varies under certain conditions. I'm not just looking for the answer but I do really want to understand how to actually solve for this so I can continue with the rest of this quiz on my own once I Have my head wrapped around the principle. THank you!